Abstract
We establish some “number theoretical” results about a continuous functionh from the circleT into itself, which generalize Kronecker’s theorem in several ways. These results are used to characterize the almost periodic sets of the flow on the torusT 2 generated by (θ, φ) → (θ+α, φ+h(θ)), where α is irrational. The almost periodic measures are characterized in the caseh(θ)=θ.
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Glasner, S. Almost periodic sets and measures on the torus. Israel J. Math. 32, 161–172 (1979). https://doi.org/10.1007/BF02764912
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DOI: https://doi.org/10.1007/BF02764912